Voltage drop is the decrease in voltage that occurs when current flows through a circuit. Voltage drop can be a significant issue in electrical circuits, as it can cause equipment to malfunction or fail.
Therefore, it’s important to calculate the voltage drop in a circuit to ensure that the circuit is functioning properly and safely.
In this article, we’ll explain how to calculate voltage drop in both DC and AC circuits, with examples for each calculation.
Table of Contents
DC Voltage Drop Calculation
In a DC circuit, voltage drop can be calculated using Ohm’s law, which relates voltage, current, and resistance:
V = I x R
Where: V = Voltage drop (in volts) I = Current (in amperes) R = Resistance (in ohms)
To calculate the voltage drop across a resistor in a DC circuit, you need to know the value of the resistor and the current flowing through it. Here’s an example:
Example:
Suppose we have a 10-ohm resistor in a DC circuit with a current of 2 amperes flowing through it. To calculate the voltage drop across the resistor, we can use Ohm’s law:
V = I x R V = 2 A x 10 ohms V = 20 volts
So the voltage drop across the resistor in this DC circuit is 20 volts.
AC Voltage Drop Calculation
In an AC circuit, voltage drop can be a bit more complex because of the effect of reactance on the circuit impedance.
The impedance of a component in an AC circuit is the combined effect of its resistance and reactance.
The reactance depends on the frequency of the AC current, and it can be either capacitive or inductive.
To calculate voltage drop in an AC circuit, you need to take into account the impedance of the component as well as the phase angle between the voltage and the current.
Here’s the formula for calculating voltage drop in an AC circuit:
V = I x Z x cos(θ)
Where:
V = Voltage drop (in volts) I = Current (in amperes) Z = Impedance (in ohms) θ = Phase angle between voltage and current (in degrees)
To calculate the voltage drop across a component in an AC circuit, you need to know the impedance of the component, the current flowing through it, and the phase angle between the voltage and the current. Here’s an example:
Example:
Suppose we have a 10-ohm resistor in an AC circuit with a frequency of 50 Hz. Let’s assume that the resistor is purely resistive (i.e., its reactance is zero), and that the current through the resistor is 1 ampere with a phase angle of 30 degrees. The impedance of the resistor is simply its resistance:
Z = 10 ohms
To calculate the voltage drop across the resistor, we can use the formula:
V = I x Z x cos(θ) V = 1 A x 10 ohms x cos(30) V = 8.66 volts
So the voltage drop across the resistor in this AC circuit is 8.66 volts.
The formula for calculating voltage drop in a 3-phase circuit is similar to the formula for a single-phase circuit, but it takes into account the three phases and the phase angle between them.
formula for calculating voltage drop in a 3-phase circuit:
Vd = √3 x I x L x Z x cos(Φ) / 1000
Where:
Vd = voltage drop (in volts) √3 = the square root of 3 (approx. 1.732) I = current in the circuit (in amperes) L = length of the cable (in meters) Z = total impedance of the cable (in ohms) Φ = phase angle between the current and the voltage
Note that in this formula, the impedance Z is the total impedance of the cable, including its resistance and reactance in each of the three phases.
The phase angle Φ represents the phase difference between the current and the voltage, which is affected by the cable’s reactance.
To calculate the total impedance of the cable in a 3-phase circuit, you need to take into account the resistance and reactance of the cable in each of the three phases.
If the cable has a balanced construction, where each phase has the same impedance, you can calculate the total impedance as follows:
Ztotal = Zphase x L / 1000
Where Zphase is the impedance per unit length of a single phase of the cable (in ohms/km or ohms/m), and L is the total length of the cable (in meters).
Here’s an example of how to use the 3-phase voltage drop formula:
Example:
Suppose you want to calculate the voltage drop in a 3-phase circuit with a total length of 200 meters, using a 4-core cable with a current of 50 amperes per phase.
The cable is an XLPE-insulated copper conductor with a cross-sectional area of 16 square millimeters.
The cable table lists the resistance and reactance of each phase of the cable as 1.15 ohms/km and 0.085 ohms/km, respectively.
To calculate the total impedance of the cable, you can use the formula:
Zphase = √(R^2 + X^2) = √(1.15^2 + 0.085^2) = 1.152 ohms/km Ztotal = Zphase x L / 1000 = 1.152 ohms/km x 200 m / 1000 = 0.2304 ohms
Then, you can use the voltage drop formula to calculate the voltage drop:
Vd = √3 x I x L x Z x cos(Φ) / 1000 Vd = √3 x 50 A x 200 m x 0.2304 ohms x 1 = 99.9 volts
So the voltage drop in this 3-phase circuit is 99.9 volts.
Note that the phase angle Φ is assumed to be zero in this example because the cable is not specified as having a capacitive or inductive reactance.
If the cable had a significant capacitive or inductive reactance, you would need to include the phase angle in the calculation.
Calculations using resistance and reactance of the cable
There are other formulas for calculating voltage drop in circuits that take into account the resistance and reactance of the cable.
These formulas are more commonly used in power transmission and distribution systems where the length of the cable can be quite long, and the cable impedance can significantly affect the voltage drop.
Here is the formula for calculating voltage drop using the resistance and reactance of the cable:
Vd = (I x L x (R x cos(Φ) + X x sin(Φ))) / 1000
Where:
Vd = voltage drop (in volts) I = current in the circuit (in amperes) L = length of the cable (in meters) R = resistance of the cable (in ohms/km) X = reactance of the cable (in ohms/km) Φ = phase angle between the current and the voltage
Note that in this formula, R and X are given as resistance and reactance per unit length (usually ohms/km or ohms/m). Therefore, you need to know the length of the cable in order to calculate the total resistance and reactance of the cable.
In practice, it can be difficult to determine the exact resistance and reactance of a cable, especially if the cable has a non-uniform geometry or if the insulation or jacket material affects the cable’s electrical properties.
In these cases, you may need to refer to a cable table or a cable manufacturer’s datasheet to find the resistance and reactance of the cable.
A cable table typically lists the resistance and reactance of different cable types and sizes, based on standard values for the cable’s electrical properties.
The table may also provide information on the maximum current rating, voltage rating, and other characteristics of the cable.
To use a cable table to calculate voltage drop, you need to know the length of the cable, the current in the circuit, and the cable size and type.
Here’s an example of how to use a cable table to calculate voltage drop:
Example: Suppose you want to calculate the voltage drop in a circuit with a total length of 100 meters, using a 2-core cable with a current of 10 amperes.
The cable is a PVC insulated copper conductor with a cross-sectional area of 4 square millimeters. The cable table lists the resistance and reactance of the cable as 4.61 ohms/km and 0.084 ohms/km, respectively.
To calculate the total resistance and reactance of the cable, you can multiply the resistance and reactance per unit length by the total length of the cable:
Rtotal = 4.61 ohms/km x 0.1 km = 0.461 ohms Xtotal = 0.084 ohms/km x 0.1 km = 0.0084 ohms
Then, you can use the voltage drop formula to calculate the voltage drop:
Vd = (I x L x (R x cos(Φ) + X x sin(Φ))) / 1000 Vd = (10 A x 100 m x (0.461 x 1 + 0.0084 x 0)) / 1000 Vd = 4.61 volts
So the voltage drop in this circuit is 4.61 volts.
Note that the phase angle Φ is assumed to be zero in this example because the cable is not specified as having a capacitive or inductive reactance.
If the cable had a significant capacitive or inductive reactance, you would need to include the phase angle in the calculation.
Thankfully, there are now mobile applications available that can help with this process. One such app is Cables Tables, install it from google play, which provides a comprehensive database of cables, including their size, voltage drop tables, and derating factors tables. I made this app myself to help you with your work.
Using Cables Tables app can save you time and effort in finding the right cable for your circuit and help you determine the voltage drop accurately.
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